Approximation numbers of weighted composition operators

We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators wit...

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Bibliographic Details
Authors: Lechner, Gandalf, Li, Daniel, Queffélec, Hervé, Rodríguez Piazza, Luis
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2018
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69957
Online Access:https://hdl.handle.net/11441/69957
https://doi.org/10.1016/j.jfa.2018.01.010
Access Level:Open access
Keyword:Composition operators
Approximation numbers
von Neumann algebras
Description
Summary:We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).